Deputy Prime Minister Nick Clegg will fire the starting gun in the Liberal Democrats' Eastleigh by-election campaign later with a promise to press for higher taxes on the wealthy to ease the burden on "hard-working families".

In the Commons, Lib Dem chief whip Alistair Carmichael will move the writ formally triggering the contest to elect a successor to disgraced former Cabinet minister Chris Huhne.

Polling will take place in just three weeks' time, on February 28, in a battle which will pitch the Lib Dems into a head-to-head fight with their coalition partners, the Tories, who finished second in the 2010 general election.

Both parties are braced for a bruising contest, with Conservative Party chairman Grant Shapps signalling that they intend to focus on Huhne's past after he pleaded guilty in court to dodging punishment for a speeding offence, saying: "The residents of Eastleigh have for a long time been sold a lie by their Lib Dem MP. That's why they'll welcome the opportunity to express the way they feel about it very soon."

Lib Dems insisted their decision, as the sitting party in the constituency, to opt for a short contest reflected the high state of preparedness of the local party, even though they have yet to choose a candidate. Mr Clegg is expected to travel to the Hampshire constituency to campaign as soon as he can clear the space in his diary. Officials would not be drawn on whether he would offer an apology for Huhne's conduct, but acknowledged that he would have to deal with the issue.

Officially, the Lib Dems want to make jobs and taxes the key campaign issues - drawing clear battlelines with the Conservatives. Mr Clegg will use a speech at the Institute for Government in London to highlight the Lib Dems' commitment to a 1% annual "mansion tax" on properties worth over £2 million - a proposal the Tories have consistently rejected. He will say the Lib Dems want new council tax bands at the top end, again affecting properties worth more than £2 million.

Simon Hughes, deputy leader of the Lib Dems, said the party will be "all guns blazing" at the next by-election. Speaking on Daybreak he said: "I think people increasingly do know that it's us who've delivered the tax cuts. It's the most important thing you can do, to put money back in the hands and the pockets of families who are struggling to pay the bills."

Asked whether Chris Huhne had damaged the image of the party, he said: "Of course it is a very unsatisfactory state of affairs, both for him and his family, and for the party. He's resigned as MP, we fight a by-election. Chris Huhne paid the penalty, we move on."

The Lib Dems will select their candidate at a private hustings on Saturday. There is speculation that the Tory candidate will be Maria Hutchings, who fought the seat in 2010. Labour sources are hoping for a strong showing, but privately accept they have little chances of winning.

The campaign was formally started as the writ for the contest was moved in the Commons by Lib Dem chief whip Alistair Carmichael.